In: Stilla U et al (Eds) PIA07. International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, 36 (3/W49B)
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MULTIBASELINE INTERFEROMETRIC SAR AT MILLIMETERWAVES
TEST OF AN ALGORITHM ON REAL DATA AND A SYNTHETIC SCENE
H. Essen a, T. Brehm a, S. Boehmsdorff b, U. Stilla c
a
FGAN, Research Institute for High Frequency Physics and Radar Techniques, D-53343 Wachtberg, Germany –
(essen, brehm)@fgan.de
b
Technical Center of the German Armed Forces, Oberjettenberg, D-76275 Schneizlreuth, Germany Stephanboehmsdorff@bwb.org
c
Technical University Munich, Arcisstr. 21, D-80290 München, Germany Stilla@bv.tum.de
KEY WORDS: Millimeterwaves, Interferometry, Synthetic Aperture Radar, Phase unwrapping
ABSTRACT:
Interferometric Synthetic Aperture Radar has the capability to provide the user with the 3-D-Information of land surfaces. To gather
data with high height estimation accuracy it is necessary to use a wide interferometric baseline or a high radar frequency. However
the problem of resolving the phase ambiguity at smaller wavelengths is more critical than at longer wavelengths, as the unambiguous
height interval is inversely proportional to the radar wavelength. To solve this shortcoming a multiple baseline approach can be used
with a number of neighbouring horns and an increasing baselength going from narrow to wide. The narrowest, corresponding to
adjacent horns, is then assumed to be unambiguous in phase. This initial interferogram is used as a starting point for the algorithm,
which in the next step unwraps the interferogram with the next wider baseline using the coarse height information to solve the phase
ambiguities. This process is repeated consecutively until the interferogram with highest precision is unwrapped. On the expense of
this multi-channel-approach the algorithm is simple and robust, and even the amount of processing time is reduced considerably,
compared to traditional methods. The multiple baseline approach is especially adequate for millimeterwave radars as antenna horns
with relatively small aperture can be used while a sufficient 3-dB beamwidth is maintained.
The paper describes the multiple baseline algorithm and shows the results of tests on a synthetic area. The test objects are
representative in size for generic buildings. Possibilities and limitations of this approach are discussed. The relevance for
applications of millimeterwave InSAR as means for the extraction of characteristics of buildings is highlighted. Examples of digital
elevation maps derived from measured data are shown.
KURZFASSUNG:
Mit interferometrischem SAR können dreidimensionale Informationen über Landoberflächen gewonnen werden. Um Daten mit
hoher Höhenschätzgenauigkeit gewinnen zu können, muss entweder eine große interferometrische Basis gewählt oder bei geringerer
Basisbreite eine höhere Betriebsfrequenz verwendet werden. Bei höherer Radarfrequenz ist jedoch das Problem der
Phasenfortsetzung schwieriger zu lösen, da das eindeutig bestimmbare Höhenintervall invers proportional zur Frequenz ist. Um
diesen Nachteil auszugleichen, kann ein Multibasenansatz verwendet werden, der mehrere benachbarte Sende-/Empfangshörner mit
zunehmender Basisbreite nutzt. Für die geringste Basisbreite sollte die Phasenbeziehung eindeutig sein. Das zugehörige
Interferogramm wird als Ausgangsdatensatz für ein rekursives Verfahren genutzt, bei dem die Grobinformation des ungenaueren
Interferogramms als Basis für das nächst feinere Interferogramm dient. Mit dem Nachteil des höheren Hardwareaufwandes ergibt
sich hier ein sehr einfacher und dabei schnell arbeitender Ansatz für den Phasenfortsetzungsalgoritmus. Der Mehrbasenansatz ist
besonders für den Millimeterwellenbereich geeignet, da hier Antennenhörner mit relativ geringer Apertur bereits eine ausreihende
Bündelung bieten.
Der Beitrag beschreibt den Mehrbasenalgoritmus und zeigt Ergebnisse für eine generische Testszene. Die Bedeutung dieser Methode
für die Bestimmung der Höhencharakteristik von Gebäuden wird besprochen. Vor- und Nachteile dieses Ansatzes werden diskutiert
und Beispiele erläutert.
systems with all-weather capability, millimeterwave radars are
the prime choice. In addition to the compactness of the
millimetric hardware, for which even integrated subsystems on
GaAs-basis are feasible, very simple and straight-forward
signal-processing techniques can be used at millimeterwave
frequencies. This is mainly due to three reasons (Boehmsdorff,
S., 1989): The aperture length of the SAR is reduced by the
1.INTRODUCTION
Requirements for forces engaged in peacekeeping and antiterror missions demand reconnaissance systems with allweather capability delivering in-time information content. A
solution to these requirements are liteweight SAR-Systems onboard of RPVs. For the realization of compact and robust
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be a quite simple one like the Goldstein or Dipole algorithm [2],
if the height variation of the imaged area doesn’t exceed the
unambiguous height dramatically. In order to start the further
processing all available interferograms are stored and sorted
according to their baselines. The full process is tested using a
synthetic scene with a number of generic objects. This is
described in the following.
ratio of wavelengths at equal cross-range resolution, and allows
lower requirements for the flight stability of the airborne
platform. The amount of excessive backscattering at edges and
corners of man made structures is much less due to a relatively
higher geometric deviation of right angles and straightness of
lines and a higher roughness of surfaces. Interferometric SAR
at millimeterwave frequencies offers the additional advantage of
small baselines for high height estimation accuracy. However
the smaller wavelength leads also to a higher phase ambiguity,
resulting in a much higher amount of sophistication for phase
unwrappin at these radar bands.
To overcome this shortcoming, a hardware approach has been
developed using multiple baselines to deliver interferograms at
different height estimation precision ranging from low to high.
This approach is adequate for millimeterwaves as those
different baselines can be accommodated within small
geometric dimensions. For classical radar bands this can not be
achieved within dimensions typical for RPVs.
3.DESCRIPTION OF SYNTHETIC TEST AREA
The test area described here is an artificial data set, created by a
program written in Matlab®. Its dimension is 1000 × 2000
pixels, and it contains several sample objects of different
heights and shapes. In particular there are seven generic objects
to test the unwrapping algorithm and in addition two noise
patches. All objects are located on a flat plane. A picture of the
elevation model, which is described qualitatively in the
following, is shown in Fig. 2.
2.A MULTIPLE BASELINE APPROACH FOR
MILLIMETERWAVE INTERFEROMETRIC SAR
2.1 Hardware Assembly
The millimeterwave radar system for which the algorithm has
been developed (Boehmsdorff, S., 2001) is equipped with a
multibaseline antenna consisting of an array of six horns
followed by a cylindrical lens, which achieves the azimuthal
beamforming. The antenna has a 3 dB beam width of 3° in
azimuth and 12° in elevation. A photo of the antenna
arrangement is shown in Fig 1. E1 – E4 denote the four
receiving channels, S1 and S2 the two possible transmitting
ports.
Figure 2: Elevation model of the test area. Noise patches are
shown as white holes in the plane.
E1
The first object at the upper left corner is a set of three
mountains of Gaussian shape and different height and width
neighboured by a round pillar. Below these there is a box,
representing a man made object like a building, with a noise
patch in the back simulating the shadow of the object. The next
object is a round noise patch resembling a water surface were
the backscattering tends to be of specular character and the
phase appears noisy. Then a ramp is leading below the plane
like a pit. Two rectangular pillars of different heights and an
increasing ramp above a rectangular cross section complete the
synthetic test area. For this test area the effectiveness of a new
phase unwrapping technique, based upon an approach using
more than two receiver channels at increasing interferometric
basewidth will be evaluated.
E2
S1
E3
S2
E4
4.DISCUSSION OF BASIC INTERFEROGRAMS
Figure 1: Radar Front - End with Multiple Baseline Antenna
From this elevation model five interferograms were calculated
for a baseline ratio of 1:2:3:4:5 relative to the first one. For the
test it is assumed that the reference interferogram is
unambiguous. All other interferograms are allowed to exhibit as
many phase excursions as appropriate for the respective height.
Due to the baseline ratios they are limited to five. In addition
all simulated interferograms are corrupted with white noise of
± 15 ° to resemble a typical measured data set. The phase values
corresponding to the ground-plane are allowed to exhibit an
arbitrary offset relative to each other. The five interferograms
are show in Figs. 3-7. To localize the noise patches the pseudo
correlation map is rather used. The pseudo correlation map
(Ghiglia, D. C., 1998) can be used as a quality criterion when
From each receiver channel complex data are retrieved. Due to
the geometry of the horn ensemble five independent
interferograms can be extracted.
2.2 Basic Phase Unwrapping
The phase unwrapping method based upon this hardware
approach needs at least one unambiguous interferogram, which
is usually the one corresponding to the smallest baseline. In
case that this one is not unambiguous, it is necessary to unwrap
it with an algorithm based upon a different approach. This can
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In: Stilla U et al (Eds) PIA07. International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, 36 (3/W49B)
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the magnitudes of the complex values are unknown. It is
defined by:
(∑ cos ϕ ) + (∑ sin ϕ )
2
z m ,n =
i, j
2
i, j
k2
(1)
The two sums are evaluated in an interval of the dimension k x
k around each pixel (m,n). The values of ϕi,j are the phase
values of the interferograms. Therefore this quality map is
always available, even if only the phase differences are know.
Within the correlation map points of low correlation indicate
areas where the phase is decorrelated. These regions are noisy
patches, like shadow areas or any region which shows specular
reflectance. As an example Fig. 8 depicts the pseudo correlation
map for the interferogram with the widest baseline shown in
Fig. 7.
Figure 7: as Fig. 3,
Baseline 5
Figure 3: Interferogram,
Baseline 1
Figure 8: Pseudo correlation map related to Fig. 7
The chart of Fig. 8 shows clearly the areas of low correlation
within the noisy patches. In addition the limits of the box, the
two pillars and the descending ramp are marked as areas of low
correlation because of the considerable phase variation,
although the phase within that limits is well defined. The border
of the ascending ramp is marked with dashed lines which is due
to the periodic correlation of the phase values (modulo 2π)
while the phase values are increasing in comparison to that of
the ground plane. Although the pseudo correlation map has the
disadvantage of indicating steep terrain as low correlated it can
be used as a tool to guide the phase unwrapping algorithm. In
the example it serves to define areas where phase unwrapping is
possible. After creating the interferograms at increasing basewidth it is possible to establish the unwrapping algorithm.
Figure 4: as Fig. 3,
Baseline 2
5.PHASE UNWRAPPING ALGORITHM FOR
MULTIPLE BASELINE INSAR DATA
5.1 Description of the Process
Figure 5: as Fig. 3,
Baseline 3
As mentioned under 2.2 the algorithm needs at least one
unambiguous interferogram as an initial starting point. It is
postulated for the evaluation process, that the first
interferogram, related to the narrowest baseline, is
unambiguous. For further processing all interferograms are
sorted according to their baselines. The unwrapping algorithm
works iteratively using one interferogram after the other. From
the preceding interferogram a look-up table is generated and
used for unwrapping the next interferogram with higher
interferometric base width where the phase is ambiguous but
exhibits a higher precision. This is repeated until all
interferograms are processed successively. It has to be pointed
out, that unlike in the usual residues approach, no paths around
ambiguous areas have to be searched to unwrap the phase. All
undefined pixels within the resulting interferogram are strongly
restricted to their location, and there is no error spread in the
image plane. Errors that occur are mainly due to excessive
phase noise. Due to the scaling of the successive interferograms
which has to be done during the unwrapping process, the noise
contributions are also scaled by the same ratio and therefore
Figure 6: as Fig. 3,
Baseline 4
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Within all figures the gray scale is the same, where black
represents –π and white π. The algorithm starts with the first
channel combination and unwraps all following ones. To
visualize the success of the coarse to fine unwrapping process
Fig. 10 shows the raw phase as vertical profile related to the
synthetic area and Fig. 11 the corresponding unwrapped phase.
It can be seen that the algorithm leaves most values untouched
except at those positions where the phase is wrapped around. It
has to be pointed out, that the algorithm presented here works
fully automatically after choosing the input parameters and
provides the user with five interferograms of different quality
that have no or only a few residues left outside the noisy
patches of shadow areas.
erroneous pixels may occure. To solve this problem, the
algorithm searches for suspicious isolated pixels within the
resultant interferogram. For those pixels a test procedure
determines if adding ± 2π gives a better result matching them to
the surrounding pixels. The flow chart of the unwrapping
algorithm is given in Fig. 9.
Read
Amplitude
and Phase
Data
Number of
Interferograms
Sorting
for Baseline
Calculating scaling
factor and scaling of
coarse interferogram
Calculation of
interval for the fine
interferogram
Figure 10: Vertical Profile of raw Phases
Adding (2 π * intervall) to
the fine interferogram
Set unwrapped interferogram
as coarse interferogram and
proceed with next baseline
combination
Removing
suspicuous pixles?
no
yes
Detecting and
removing
suspicuous pixles
Figure 11: Vertical Profile gained by Coarse to Fine Process
no
Last
interferogram?
5.2 Comparison with a Conventional Unwrapping Method
yes
To demonstrate the advantage of the new coarse to fine
unwrapping process (C2F) a conventional unwrapping method
using residues has been applied to the model scene. Fig. 12
shows the comparison. It is obvious, that at those parts of the
interferogram, where noise patches or even singular noise pixels
appear the conventional method runs into problems and errors
are spreading into the interferogram. To eliminate them a
special treatment has to be done. The C2F-method does not
suffer from such difficultties. As demonstrated under chapter
5.1 a vertical profile through the interferogram plane has been
calculated and is shown in Fig. 13. It shows the difficulties for
the Dipole method to cope with certain features of the
Hand over of all unwrapped
interferograms to memory
Figure 9: Flow chart of the unwrapping algorithm
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interferogram, namely holes in the plane and increasing ramps
with multiple phase periods. Comparing the calculation time
requirements it turns out, that the C2F Algorithm is about ten
times faster than the conventional process.
Figure 14: (left) Residue Chart, negative Values = white,
positive Values = black, (right) Representation of the Way
Chart, allowed Ways = grey, Not allowed Ways = white
6.SUMMARY
At mm-wave frequencies even with moderate baselines, i.e. in
the order of 30 cm, a good height estimation is possible, which
is appropriate to resolve the shape of man-made objects. On the
other hand a severe disadvantage is the high height ambiguity
due to the short phase repetition frequency at mm-wavelengths.
So much emphasis has to be put into the phase-unwrapping
algorithm. Appropriate for the possibility of small geometrical
dimensions and ease of processing is the hardware approach of
a multiple baseline antenna which makes the employment of the
described coarse-to-fine algorithm possible. Because scaling is
important for this process an appropriate ratio of consecutive
baselines is essential. Good results can be achieved with a ratio
of 5. Nevertheless the limitation of this algorithm is, that one
initial unambiguous interferogram is necessary to start with. As
the absolute phase variation in each unwrapped interferogram is
constant, the relative phase variation becomes smaller within
each of the consecutively unwrapped interferograms. The
system and the algorithm presented here, is a suitable approach
for mm-wave frequencies where the dimension of the
multibaseline antenna itself does not exceed that of the sensor
front-end.
Figure 12: Comparison of Results of C2F-process and
conventional Dipole Method
7.REFERENCES
Boehmsdorff, S., 1989. MEMPHIS an Experimental Platform
for Millimeterwave Radar, DGON Intl. Conf. on Radar,
München 1998, pp. 405-411
Boehmsdorff, S., 2001. Detection of Urban Areas in
Multispectral Data, IEEE/ISPRS Joint Workshop on Remote
Sensing and Data Fusion over Urban Areas, 2001
Figure 13: Vertical Profile gained by Dipole Method
Ghiglia, D. C., 1998. Two-Dimensional Phase Unwrapping,
John Wiley & Sons , Inc. New York, 1998
Fig. 14 shows a section of the residue chart for the circular
region incorporating phase noise contributions in comparison
with the corresponding section of the way chart. The latter
describes the path which may not be exceeded by the phase
unwrapping process.
The example shows, that even with multiple folding of the
interval [-π, π] the algorithm delivers correct values, as long as
the interferogram is unambiguous. The method avoids a time
consuming calculation of the adequate integration path with the
expense of a higher amount of hardware. It has further to be
pointed out, that there is no error continuation within the image
plane as with residue based methods, and all erroneous values
stay strictly limited to its vicinity.
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